Then, the vanishing lemma [1]} implies that \(\Vert u_{n}\Vert _{r}\rightarrow 0\ \text{as}\ n\rightarrow \infty \)  for any \(2<r< 2_s^{*}.\) 
Hence,
\(\int _{\mathbb {R}^{N}}m(x)|u_{n}|^{\frac{4s}{N}+2}dx\rightarrow 0 \text{ as }\ n\rightarrow \infty .\) 
